[GiNaC-list] series((x+x^2)^2,x,0) is broken

[Richard B. Kreckel]

On 6/25/23 19:34, Vladimir V. Kisil wrote:
>>>>>> On Sat, 24 Jun 2023 20:17:27 +0200, "Richard B. Kreckel" <kreckel at in.terlu.de> said:
> 
>      RK> Dear Vitaly, Thanks for your excellent treatise on the subject!
> 
>      RK> On 6/24/23 19:28, Vitaly Magerya wrote:
>      >> This is why 1/(Order(x^n)) is not Order(x^-n), it can be
>      >> Order(x^(-n-1)), or lower.
> 
>      RK> Okay.  What would be the correct code for Order_power(x,e),
>      RK> then?  What about non-integers?
> 
>      I may be missing something, but I do not believe there is a
>    meaningful connection between orders of f(x) and 1/f(x) as big-O. For
>    example, Order(x^k*sin(1/x))=Order(k) at x=0  but
>    Order(x^{-1}/sin(1/x)) is not finite.

Now, I may be missing something:
Isn't Order(x^k*sin(1/x))==Order(x^k) at x==0?
And isn't Order(x^-1)==Order(x)^-1 not finite either but still fine in a 
Laurent series?

   -richy.
-- 
Richard B. Kreckel
<https://in.terlu.de/~kreckel/>